To apply the properties of integer exponents and generate an equivalent expression with only positive exponents, we can use the following rules:
1. Product Rule: a^m * a^n = a^(m+n)
2. Quotient Rule: a^m / a^n = a^(m-n)
3. Power of a Power Rule: (a^m)^n = a^(m*n)
4. Power of a Product Rule: (a * b)^n = a^n * b^n
Now let's apply these rules to the given expression:
80 * 435^(-2)
First, we can rewrite 435^(-2) using the Quotient Rule as 1 / 435^(2).
So, the expression becomes:
80 * (1 / 435^(2))
Next, we can rewrite 1 / 435^(2) as 435^(-2) using the Power of a Power Rule.
Therefore, the expression simplifies to:
80 * 435^(-2)
Now, let's calculate the value of the expression:
80 * 435^(-2) = 80 * (1 / 435^(2))
To simplify further, we can calculate the value of 435^2:
435^2 = 435 * 435 = 189,225
Now, substituting this value back into the expression:
80 * (1 / 189,225) = 80 / 189,225
So, the expression is simplified to 80 / 189,225.